Combine water, apple cider, and golden raisins in a pot. Bring to a boil; add rice. Cook, stirring often, until most of the water is absorbed, about 17 minutes. Mix in white sugar, brown sugar, and 1/4 teaspoon cinnamon; continue cooking until rice is tender, about 3 minutes more. Remove from heat.
Heat olive oil in a large skillet over medium heat. Cook and stir apple, onion, and celery in the hot oil until softened, about 5 minutes. Season with white pepper, salt, and a dash of cinnamon. Stir in almonds; cook until starting to brown, 3 to 5 minutes.
Fold apple and almond mixture into rice. Let stand until flavors combine, about 5 minutes.